The atomic force microscope (AFM) developed in 1986 (Non-patent Document 1) is a microscope that can perform high-resolution observation of the surface topography of conductors, semiconductors, and insulators (including polymers and biomaterials). In an atomic force microscope, a pointed protrusion (tip) is attached to the end of an extremely pliable lever called a cantilever, and when this tip is brought in proximity to a sample, a very weak force generated between the sample surface and the tip can be measured via deflection of the cantilever. Unless specified otherwise, in this description the term “cantilever” is used in a broad sense that includes the tip.
When the sample surface is sufficiently soft compared with the stiffness of the cantilever of an atomic force microscope, the displacement (deflection) of the cantilever is small even though the tip comes into contact with the surface. Therefore it is difficult to measure a surface position accurately from the amount of static displacement of the tip. For example, since the lipid membrane of a cell surface is extremely soft and fluctuates with a large amplitude of several tens of nm, and its elasticity is quite small compared with a pliable cantilever normally used, it is not easy to accurately measure an elastic response or surface position of the only lipid membrane in a minimally invasive manner with an AFM.
One method of deriving a soft surface position (contact point) is to calculate the surface position from the shape of a force curve when the tip is pressed forcefully against the surface (Non-patent Document 2). Here, the force curve is a curve obtained by plotting the distance between the tip and the sample surface on the horizontal axis, and the amount of the cantilever displacement (normally, static displacement) on the vertical axis.
On the other hand, the cantilever is subject to thermal oscillation, the amplitude of which depends on the stiffness of the cantilever, but is generally on the order of 1 nm or less. Methods of utilizing the thermal oscillation of the cantilever are to estimate a spring constant of the cantilever from measurement of the spectrum of thermal oscillation (Non-patent Document 3) or to measure the interaction between the surface and the tip from the measurement of the spectrum of thermal oscillation in non-contact area (Non-patent Document 4). Non-patent Document 1: G. Binnig, C. F. Quate, and Ch. Gerber, “Atomic Force Microscope”, Phys. Rev. Lett. Vol. 56, p. 930 (1986)
Non-patent Document 2: C. Rotsch, K. Jacobson, and M. Radmacher, “Dimensional and mechanical dynamics of active and stable edges in motile fibroblasts investigated by using atomic force microscopy”, Proc. Natl. Acad. Sci. USA, Vol. 96, p. 921 (1999)
Non-patent Document 3: J. L. Hutter, J. Bechhoefer, “Calibration of atomic-force microscopetips”, Rev. Sci. Instrum. Vol. 64, p. 1868 (1993)
Non-patent Document 4: A. Roters, M. Gelbert, M. Schimmel, J. Ruhe, and D. Johannsmann, “Static and dynamic profiles of tethered polymer layers tipd by analyzing the noise of an atomic force microscope”, Phys. Rev. E Vol. 56 p. 3256 (1997)